scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

Finite-time H∞ synchronization of semi-Markov jump Lur’e systems

2021 ◽  
pp. 2150168
Author(s):  
Xin Huang ◽  
Youmei Zhou ◽  
Muyun Fang ◽  
Jianping Zhou ◽  
Sabri Arik
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Time Synchronization ◽  
Control Method ◽  
Design Method ◽  
External Disturbance ◽  
Feedback Controller ◽  
Markov Jump ◽  
Lur’E Systems ◽  
State Feedback Controller

This paper investigates the problem of finite-time [Formula: see text] synchronization for semi-Markov jump Lur’e systems with time-varying delay and external disturbance. The purpose of this work is to design a mode-dependent state-feedback controller to ensure that the synchronization-error system achieves finite-time synchronization with a prescribed [Formula: see text] performance index. A criterion for the finite-time synchronization is proposed by using appropriate Lyapunov functional and two recently developed inequalities. Then, a design method for the required state-feedback controller is presented with the application of several decoupling techniques. Finally, an example is provided to illustrate the applicability of the proposed control method.

scholarly journals Intra-layer Synchronization in a Duplex Networks with Noise

2021 ◽  
Author(s):  
Jinsen Zhuang ◽  
Yan Zhou ◽  
Yonghui Xia
Keyword(s):  
Dynamical System ◽  
State Feedback ◽  
Feedback Controller ◽  
The Other ◽  
Time Varying ◽  
Stochastic Perturbations ◽  
State Feedback Controller ◽  
Control Schemes ◽  
Simulation Results ◽  
The Impact

This paper concerns the impact of stochastic perturbations on the intra-layer synchronization of the duplex networks. A duplex network contains two layers ([1,2]). Different from the previous works, environmental noise is introduced into the dynamical system of the duplex network. We incorporate both the inter-layer delay and the intra-layer delay into the dynamical system. Both of the delays are time-varying. However, the paper [1] only considered the intra-layer delays and they are assumed as the constants. While the paper [2] did not consider the inter-layer delay or intra-layer delay. When the system does not achieve automatic intra-layer synchronization, we introduce two controllers: one is the state-feedback controller, the other is the adaptive state-feedback controller. Interestingly, we find that the intra-layer synchronization will achieve automatically if the inter-layer coupling strength $c_1$ is large enough when the time-varying inter-layer delays are absent. Finally, some interesting simulation results are obtained for the Chua-Chua chaotic system with application of our theoretic results, which show the feasibility effectiveness of our control schemes.

scholarly journals Robust Mixed H2/H∞ State Feedback Controller Development for Uncertain Automobile Suspensions with Input Delay

Processes ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 359
Author(s):  
Nan Liu ◽  
Hui Pang ◽  
Rui Yao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Actuator Saturation ◽  
Output Feedback Control ◽  
Active Suspension ◽  
Feedback Controller ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Feedback Controller

In order to achieve better dynamics performances of a class of automobile active suspensions with the model uncertainties and input delays, this paper proposes a generalized robust linear H2/H∞ state feedback control approach. First, the mathematical model of a half-automobile active suspension is established. In this model, the H∞ norm of body acceleration is determined as the performance index of the designed controller, and the hard constraints of suspension dynamic deflection, tire dynamic load and actuator saturation are selected as the generalized H2 performance output index of the designed controller to satisfy the suspension safety requirements. Second, a generalized H2/H∞ guaranteed cost state-feedback controller is developed in terms of Lyapunov stability theory. In addition, the Cone Complementarity Linearization (CCL) algorithm is employed to convert the generalized H2/H∞ output-feedback control problem into a finite convex optimization problem (COP) in a linear matrix inequality framework. Finally, a numerical simulation case of this half-automobile active suspension is presented to illustrate the effectiveness of the proposed controller in frequency-domain and time-domain.

H∞ fuzzy proportional integral state feedback controller of photovoltaic systems under asymmetric actuator constraints

2020 ◽  
pp. 014233122092157
Author(s):  
K Houda ◽  
D Saifia ◽  
M Chadli ◽  
S Labiod
Keyword(s):  
State Feedback ◽  
Reference Model ◽  
Tracking Error ◽  
Control Design ◽  
Atmospheric Condition ◽  
Boost Converter ◽  
Feedback Controller ◽  
Duty Ratio ◽  
Linear Matrix ◽  
State Feedback Controller

This paper presents a new strategy for a robust maximum power point (MPP) tracking fuzzy controller for photovoltaic (PV) systems subject to actuator asymmetric saturation. A DC-DC boost converter is used to connect a PV panel with an output load. The output voltage of the DC-DC boost converter can be adjusted by duty ratio that is limited between 0 and 1. The aim of our control design is to track the MPP under atmospheric condition changes and the presence of the asymmetric saturation of the duty ratio. To minimize tracking error and disturbance effect, the dynamic behaviour of a PV system and its reference model are described by using Takagi–Sugeno fuzzy models. Then, a constrained control based on a fuzzy PI state feedback controller is proposed. The H∞ control approach is used in control design and stability conditions of the closed-loop system are formulated and solved in terms of linear matrix inequalities. Finally, simulation results are given to show the tracking performance of the control design.

Performance Comparison between PID Controller and State-Feedback Controller with Integral Action in Position Control of DC Motor

2013 ◽  
Vol 367 ◽  
pp. 188-193
Author(s):  
A. Chowdhury ◽  
D. Debnath
Keyword(s):  
Pid Controller ◽  
State Feedback ◽  
Position Control ◽  
Performance Comparison ◽  
Feedback Controller ◽  
System Response ◽  
Feedback Gain ◽  
State Feedback Controller ◽  
Integral Action ◽  
The Time Domain

This paper presents the design of PID controller and State-Feedback controller with integral action to control the position of DC motor.PID controller is tuned using Ziegler-Nichol’s rules. State-Feedback controller is designed by determining the state feedback gain matrix using Ackermann’s formula. The aim of this paper is to compare the time domain characteristics of system response between PID controller and State feedback Controller with integral action. The Simulation results are demonstrated using MATLAB.Graphical User Interface (GUI) is developed for both the controllers. According to the Simulation result, State-Feedback controller with integral action has the better performance in terms of peak overshoot and settling time as compared to PID controller.

scholarly journals Active Vibration Control of Container Cranes against Earthquake by the Use of LMI Based MixedH2/H∞State-Feedback Controller

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
C. Oktay Azeloglu ◽  
Ahmet Sagirli
Keyword(s):  
State Feedback ◽  
Active Vibration Control ◽  
Time History ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Container Cranes ◽  
State Feedback Controller ◽  
Active Vibration ◽  
Control Forces ◽  
Six Degree Of Freedom

This paper studies the design of a linear matrix inequality (LMI) based mixedH2/H∞state-feedback controller for vibration attenuation problem of seismic-excited container cranes. In order to show effectiveness of the designed controller, a six-degree-of-freedom container crane structural system is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motion of El Centro and Northridge earthquakes. Finally, the time history of the crane parts displacements, accelerations, control forces, and frequency responses of both uncontrolled and controlled cases are presented. Additionally, the performance of the designed controller is also compared with a nominal state-feedbackH∞controller performance. Simulations of the designed controller show better seismic performance than a nominal state-feedbackH∞controller. Simulation results show that the designed controller is all effective in reducing vibration amplitudes of crane parts.

scholarly journals Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yucai Ding ◽  
Hui Liu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Reachable Set ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
State Feedback Controller ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

The problems of reachable set estimation and state-feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state-feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

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